A perturbation analysis of stochastic matrix Riccati diffusions

Understand

Matrix differential Riccati equations are central in filtering and optimal control theory.

• The purpose of this article is to develop a perturbation theory for a class of stochastic matrix Riccati diffusions.
• Diffusions of this type arise, for example, in the analysis of ensemble Kalman-Bucy filters since they describe the flow of certain sample covariance estimates.
• In this context, the random perturbations come from the fluctuations of a mean field particle interpretation of a class of nonlinear diffusions equipped with an interacting sample covariance matrix functional.